First edition of these expanded presentations of the ideas in de Broglie’s epoch-making doctoral thesis on the quantum theory, which, Einstein said, “lifted a corner of the great veil” (Isaacson, Einstein: His Life and Universe, p. 327). In that work he developed the startling and revolutionary idea that material particles such as electrons have a wave as well as a corpuscular nature, analogous to the dual behavior of light demonstrated by Einstein and others in the first two decades of the twentieth century. “He made the leap in his September 10, 1923, paper [‘Ondes et quanta,’ Comptes Rendus, t. 177]: E = hν should hold not only for photons but also for electrons, to which he assigns a ‘fictitious associated wave’” (Pais, Subtle is the Lord, p. 436). “Louis de Broglie achieved a worldwide reputation for his discovery of the wave theory of matter, for which he received the Nobel Prize for physics in 1929. His work was extended into a full-fledged wave mechanics by Erwin Schrödinger and thus contributed to the creation of quantum mechanics” (DSB). De Broglie was awarded the 1929 Nobel Prize in physics “for his discovery of the wave nature of electrons.” De Broglie’s book Ondes et mouvements (1926) was selected by Carter and Muir for the Printing and the Mind of Man exhibition and catalogue (1967).

In his 1905 paper ‘Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt’ (‘On a Heuristic Viewpoint Concerning the Production and Transformation of Light’), “Einstein postulated that light is composed of individual quanta (later called photons) that, in addition to wavelike behavior, demonstrate certain properties unique to particles. In a single stroke he thus revolutionized the theory of light and provided an explanation for, among other phenomena, the emission of electrons from some solids when struck by light, called the photoelectric effect” (Britannica). “The central idea of de Broglie’s work … was that the formula E = hν by which Einstein had related the frequency ν of light to the energy E of light quanta should not only apply to light but also to material particles. For a particle at rest with mass m he concluded, since its energy is E = mc2, that it performs an internal oscillation with frequency ν = mc2/h. He considered the motion of a particle, carefully taking into account the effects of the special theory of relativity, and was able to construct a wave which was always in phase with the internal oscillation of the particle … he gave an application of his theory by showing that he could naturally explain the discrete electron orbits in Bohr’s model of the hydrogen atom. Each stable orbit should be closed in the sense that the same phase should be assumed by the matter wave after completion of an orbit” (Brandt, The Harvest of a Century, Chapter 32, p. 133).

In a second Comptes Rendus note, De Broglie also predicted on the basis of his theory that ‘a stream of electrons traversing a very small aperture will show the phenomenon of diffraction.’ This was experimentally observed by C. J. Davisson and L. H. Germer in 1927, work for which they received the Nobel Prize in Physics in 1937. “Thus the duality of both light and matter had been established, and physicists had to come to terms with fundamental particles which defied simple theories and demanded two sets of 'complementary' descriptions, each applicable under certain circumstances, but incompatible with one another” (PMM 417). Finally, in a third note, De Broglie derived from his theory “a result of Planck on the kinetic theory of gases, by making the assumption that ‘the state of a gas will be stable only if the waves corresponding to all the atoms form a system of stationary waves.’ He also showed that “the interplay between the propagation of a particle and of its associated matter wave could be expressed in more formal terms as an identity between the fundamental variational principles of Pierre de Fermat (rays), and Pierre Louis Maupertuis (particles)” (DSB).

When de Broglie first published his theory of matter waves he was practically unknown in scientific circles, although his elder brother Maurice had already done important experimental work on X-rays and his illustrious family was famous in France. His ideas became widely known only with the publication of his doctoral thesis Recherches sur la théorie des quanta in the summer of 1924, which is an elaboration of the content of the three Comptes Rendus notes. Einstein’s support for de Broglie’s ideas brought them to the attention of the principal actors in the development of quantum theory, notably Schrödinger, whose wave mechanics was an extension and completion of de Broglie’s work. An account of Schrödinger’s development of de Broglie’s ideas into what became wave mechanics is given in the 1928 work offered here.

“In his communications of 1923, and later in his 1924 PhD thesis, de Broglie did not want to commit himself to any physical interpretation of the waves. He granted physical relevance only to these wave features which could be directly related to the particle motion, namely their phase, while eluding any questions pertaining to their amplitude and proper dynamics. They were, as he dubbed them, “fictitious.” However, in the months following his PhD, de Broglie started to explore the consequences of his wave-particle model for the problem of the interaction of light with matter. He also considered the possibilities of more physically interpreting his particle-associated waves. Willing to acknowledge the reality of the particles, he tried to conceive them as embodied by the singularities of the waves. However, he had then to cope with the Schrödinger view, where only continuous matter waves were considered. He first attempted to save his dualism by conceiving Schrödinger’s equation as actually admitting pairs of solutions characterized by a common phase. He thought of each pair as consisting of a singular solution, with the singularity identified with the particle, while the corresponding continuous regular solution (the only one considered by Schrödinger) was interpreted as conveying solely statistical information. In this approach, the probabilistic (Max Born's) interpretation of the continuous wave reflected the inherent neglect of the singularity (the particle). This so-called double-solution interpretation was hence a causal one, conceiving Schrödinger waves as conveying all the potential outcomes, while concealing the realities of the underlying particle dynamics. These dynamics were non-classical, owing to the fundamental fact that the particle was coupled to the wave via the guiding mechanism which related the particle’s velocity to the gradient of the wave phase” (DSB). “In early 1926, Louis de Broglie published a book, Ondes et Mouvements, in which he outlined the main results of his ‘phase wave’ approach to atomic theory” (Mehra & Rechenberg, Historical Development of Quantum Theory, Vol. 5, p. 686, n. 105).

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First edition of these expanded presentations of the ideas in de Broglie’s epoch-making doctoral thesis on the quantum theory, which, Einstein said, “lifted a corner of the great veil” (Isaacson, Einstein: His Life and Universe, p. 327). In that work he developed the startling and revolutionary idea that material particles such as electrons have a wave as well as a corpuscular nature, analogous to the dual behavior of light demonstrated by Einstein and others in the first two decades of the twentieth century. “He made the leap in his September 10, 1923, paper [‘Ondes et quanta,’ Comptes Rendus, t. 177]: E = hν should hold not only for photons but also for electrons, to which he assigns a ‘fictitious associated wave’” (Pais, Subtle is the Lord, p. 436). “Louis de Broglie achieved a worldwide reputation for his discovery of the wave theory of matter, for which he received the Nobel Prize for physics in 1929. His work was extended into a full-fledged wave mechanics by Erwin Schrödinger and thus contributed to the creation of quantum mechanics” (DSB). De Broglie was awarded the 1929 Nobel Prize in physics “for his discovery of the wave nature of electrons.” De Broglie’s book Ondes et mouvements (1926) was selected by Carter and Muir for the Printing and the Mind of Man exhibition and catalogue (1967).

In his 1905 paper ‘Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt’ (‘On a Heuristic Viewpoint Concerning the Production and Transformation of Light’), “Einstein postulated that light is composed of individual quanta (later called photons) that, in addition to wavelike behavior, demonstrate certain properties unique to particles. In a single stroke he thus revolutionized the theory of light and provided an explanation for, among other phenomena, the emission of electrons from some solids when struck by light, called the photoelectric effect” (Britannica). “The central idea of de Broglie’s work … was that the formula E = hν by which Einstein had related the frequency ν of light to the energy E of light quanta should not only apply to light but also to material particles. For a particle at rest with mass m he concluded, since its energy is E = mc2, that it performs an internal oscillation with frequency ν = mc2/h. He considered the motion of a particle, carefully taking into account the effects of the special theory of relativity, and was able to construct a wave which was always in phase with the internal oscillation of the particle … he gave an application of his theory by showing that he could naturally explain the discrete electron orbits in Bohr’s model of the hydrogen atom. Each stable orbit should be closed in the sense that the same phase should be assumed by the matter wave after completion of an orbit” (Brandt, The Harvest of a Century, Chapter 32, p. 133).

In a second Comptes Rendus note, De Broglie also predicted on the basis of his theory that ‘a stream of electrons traversing a very small aperture will show the phenomenon of diffraction.’ This was experimentally observed by C. J. Davisson and L. H. Germer in 1927, work for which they received the Nobel Prize in Physics in 1937. “Thus the duality of both light and matter had been established, and physicists had to come to terms with fundamental particles which defied simple theories and demanded two sets of 'complementary' descriptions, each applicable under certain circumstances, but incompatible with one another” (PMM 417). Finally, in a third note, De Broglie derived from his theory “a result of Planck on the kinetic theory of gases, by making the assumption that ‘the state of a gas will be stable only if the waves corresponding to all the atoms form a system of stationary waves.’ He also showed that “the interplay between the propagation of a particle and of its associated matter wave could be expressed in more formal terms as an identity between the fundamental variational principles of Pierre de Fermat (rays), and Pierre Louis Maupertuis (particles)” (DSB).

When de Broglie first published his theory of matter waves he was practically unknown in scientific circles, although his elder brother Maurice had already done important experimental work on X-rays and his illustrious family was famous in France. His ideas became widely known only with the publication of his doctoral thesis Recherches sur la théorie des quanta in the summer of 1924, which is an elaboration of the content of the three Comptes Rendus notes. Einstein’s support for de Broglie’s ideas brought them to the attention of the principal actors in the development of quantum theory, notably Schrödinger, whose wave mechanics was an extension and completion of de Broglie’s work. An account of Schrödinger’s development of de Broglie’s ideas into what became wave mechanics is given in the 1928 work offered here.

“In his communications of 1923, and later in his 1924 PhD thesis, de Broglie did not want to commit himself to any physical interpretation of the waves. He granted physical relevance only to these wave features which could be directly related to the particle motion, namely their phase, while eluding any questions pertaining to their amplitude and proper dynamics. They were, as he dubbed them, “fictitious.” However, in the months following his PhD, de Broglie started to explore the consequences of his wave-particle model for the problem of the interaction of light with matter. He also considered the possibilities of more physically interpreting his particle-associated waves. Willing to acknowledge the reality of the particles, he tried to conceive them as embodied by the singularities of the waves. However, he had then to cope with the Schrödinger view, where only continuous matter waves were considered. He first attempted to save his dualism by conceiving Schrödinger’s equation as actually admitting pairs of solutions characterized by a common phase. He thought of each pair as consisting of a singular solution, with the singularity identified with the particle, while the corresponding continuous regular solution (the only one considered by Schrödinger) was interpreted as conveying solely statistical information. In this approach, the probabilistic (Max Born's) interpretation of the continuous wave reflected the inherent neglect of the singularity (the particle). This so-called double-solution interpretation was hence a causal one, conceiving Schrödinger waves as conveying all the potential outcomes, while concealing the realities of the underlying particle dynamics. These dynamics were non-classical, owing to the fundamental fact that the particle was coupled to the wave via the guiding mechanism which related the particle’s velocity to the gradient of the wave phase” (DSB). “In early 1926, Louis de Broglie published a book, Ondes et Mouvements, in which he outlined the main results of his ‘phase wave’ approach to atomic theory” (Mehra & Rechenberg, Historical Development of Quantum Theory, Vol. 5, p. 686, n. 105).